Need Advice which sharing hosting will run Magento Community fast or some other not expensive solution.

This website will not have a lot of users,
I only need that it will run fast for 100-20 users in same time.
The problem with magento is database design that make this system very slow , also other staff not the best.

I had hostmonster.com and justhost.com for previous website but it wasn't fast enough for single user that not located in USA (my customer areas: Asia, Africa).
each action that involve database takes a lot of time.

I wouldn't suggest a VPS in place of shared hosting, for a number of reasons.

Let's assume your budget is £30 per month - from bytemark.co.uk this gives you

1000MB RAM

1 CPU Core

20GB storage

The downsides of using a VPS being

You need to manage your own server. That means you have to optimise the server, monitor the server, fix any issues with the server - have you got that level of experience?

Your I/O is shared. Anyone else's activity using the common HDDs will bottleneck anything your Magento store needs to do

You are limited to 1GB RAM, to put this into perspective ...

Each PHP thread (visitor) needs an average 30MB RAM and its corresponding MySQL connection will need just a bit more. So that is 80MB per visitor. Your base OS needs about 140MB RAM to run. MySQL base wants as much as possible, but as a minimum, it will need 300MB.

So you are using 440MB, leaving you support for 7 active visitors - which is fortunate, because 1 2.5GHz core can push through a maximum of 7 requests per second (for Magento).

--

Conversely, you could pick a Magento host that already optimises its shared servers, uses external DB servers, and usually has a powerful machine that you can burst resources on, to a factor of around 8 of what your VPS offers.

There are a few Magento hosting comparison sites out there that will help you make this decision.